FRA calculation

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saborio

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Can someone please explain the different types of FRA equation (ie long/ short) and more importantly when to use each one?
 
In an FRA, long pays fixed and receives floating, short pays floating and receives fixed.
The payoff is calculated as of the end of the loan period, but settlement is at the beginning of the loan period; the payoff is discounted back to the beginning at the floating rate.
Assuming LIBOR for the floating rate (so it’s nominal, not effective), then the settlement to the long on, for example, a 3 × 5 FRA with a notional amount of $1,000,000 a fixed rate of 3.4%, and a 5-month floating rate (as of 3 months from inception) of 4.2% would be:
[(4.2% – 3.4%) × (150/360) × $1,000,000] / [1 + 4.2%(150/360)]
= $3,333.33 / [1 + 4.2%(150/360)]
=$3,276.00
The settlement to the short would be -$3,276.00.
 
Thank you.
Of course, there are many different ways they could possibly word a FRA question. I often get sent down the ‘trick’ answer route by using the incorrect days/period/settlement date etc. Can you advise me on how I should eliminate the false dates they include in the question?
 
I’ve been thinking of it as if the floating rate > FRA rate, then the borrower has the right to borrow at below market rates of interest. Whereas if the floating rate < FRA rate, then the seller has the right to lend at an above market rate of interest, therefore short receives the cash. Does this make logical sense to others?
 
Energy.71 wrote:
I’ve been thinking of it as if the floating rate > FRA rate, then the borrower has the right to borrow at below market rates of interest. Whereas if the floating rate < FRA rate, then the seller has the right to lend at an above market rate of interest, therefore short receives the cash. Does this make logical sense to others?
Click to expand...
It’s an obligation, not a right. And depending on if it’s pay-fixed or pay-variable, then the terms borrower and seller (or long and short) can be used interchangeably.
S2000magician wrote:
In an FRA, long pays fixed and receives floating, short pays floating and receives fixed.
The payoff is calculated as of the end of the loan period, but settlement is at the beginning of the loan period; the payoff is discounted back to the beginning at the floating rate.
Assuming LIBOR for the floating rate (so it’s nominal, not effective), then the settlement to the long on, for example, a 3 × 5 FRA with a notional amount of $1,000,000 a fixed rate of 3.4%, and a 5-month floating rate (as of 3 months from inception) of 4.2% would be:
[(4.2% – 3.4%) × (150/360) × $1,000,000] / [1 + 4.2%(150/360)]
= $3,333.33 / [1 + 4.2%(150/360)]
=$3,276.00
The settlement to the short would be -$3,276.00.
Click to expand...
What is the correct number of days to use? “….a 5-month floating rate (as of 3 months from inception)” Can you explain this? Is it when the forward rate expires or at the beginning of the forward rate agreement?
What does it mean when the question says the rate is based on a 180-day LIBOR but expiration is in 90 days? How come the LIBOR rate used doesn’t correspond with the number of days until expiration?
 
hei.so wrote:
Energy.71 wrote:I’ve been thinking of it as if the floating rate > FRA rate, then the borrower has the right to borrow at below market rates of interest. Whereas if the floating rate < FRA rate, then the seller has the right to lend at an above market rate of interest, therefore short receives the cash. Does this make logical sense to others?
Click to expand...
It’s an obligation, not a right. And depending on if it’s pay-fixed or pay-variable, then the terms borrower and seller (or long and short) can be used interchangeably.
S2000magician wrote:In an FRA, long pays fixed and receives floating, short pays floating and receives fixed.
The payoff is calculated as of the end of the loan period, but settlement is at the beginning of the loan period; the payoff is discounted back to the beginning at the floating rate.
Assuming LIBOR for the floating rate (so it’s nominal, not effective), then the settlement to the long on, for example, a 3 × 5 FRA with a notional amount of $1,000,000 a fixed rate of 3.4%, and a 5-month floating rate (as of 3 months from inception) of 4.2% would be:
[(4.2% – 3.4%) × (150/360) × $1,000,000] / [1 + 4.2%(150/360)]
= $3,333.33 / [1 + 4.2%(150/360)]
=$3,276.00
The settlement to the short would be -$3,276.00.
Click to expand...
What is the correct number of days to use? “….a 5-month floating rate (as of 3 months from inception)” Can you explain this? Is it when the forward rate expires or at the beginning of the forward rate agreement?
What does it mean when the question says the rate is based on a 180-day LIBOR but expiration is in 90 days? How come the LIBOR rate used doesn’t correspond with the number of days until expiration?
Click to expand...
LIBOR uses 30-day months and 360-day years.
If is says that the rate is based on 180-day LIBOR and expiration is in 90 days, it’s a 3 × 9 FRA: it expires in 3 months, and the underlying (floating-rate) loan is 180 days.
 
S2000magician, what you described is a 3 x 9 FRA. A 3 x 6 would be based on 90-day LIBOR.
regards
 
Okay. So if it’s a 3 x 6 FRA, here’s a timeline of my understanding.
Now……3 months later (FRA expires, cash settlement is made based on the beginning period rate)…….6 laters month [9 months total] (Loan expires, but this date doesn’t really matter since payment is already made at the beginning of the loan).
EDITED: Based on a 90 day LIBOR
 
Whether the 180-day LIBOR expires in 90 days or in 150 days for calculations in the exam it doesnt matter. We are only concerned if it is a 180-day LIBOR or a 150-day LIBOR or a xxx-day LIBOR, right?
 
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